高阶混合型中立差分方程解的振动性

Oscillation of Higher Order Neutral Difference Equations of Mixed Type

研究奇数阶混合类型的中立型差分方程：△ｍ（ｘｎ＋ｃｘｎ－ｈ＋ｃ＊ｘｎ－ｈ＊）＝ｑｘｎ－ｇ＋ｐｘｎ＋ｇ．得到关于解振动的一系列新的判别准则．例如：若ｍ＜ｇ＊，ｐ＞［（ｇ＊－ｍ）ｇ＊－ｍ／ｇ＊ｇ＊ ＋ｃ（ｈ＋ｇ＊－ｍ）ｈ＋ｇ＊－ｍ／（ｈ＋ｇ＊ｈ＋ｇ＊）］ｍｍ且要么ｈ＊＞ｇ＊．ｐ＋ｑ＞ｃ＊ ｍｍ·＊ｈ＊－ｇ＊）ｈ＊－ｇ＊／（ｈ＊－ｇ＊＋ｍ）ｈ＊－ｇ＊＋ｍ＊，要么ｇ＞ｃ＊（ｈ＊＋ｇ）ｈ＊＋ｇｍｍ／（ｈ＊＋ｇ＋ｍ）ｈ＊＋ｇ＋ｍ 则此方程是振动的，等等．

Odd order neutral difference equations of mixed type:△m(xn+cx_(n-h))+c*x_(n-h*))= qx_(n-g)+px_(n+g)* , have been studied. A series of new criteria for the oscillation of those equations have been established. For example: assume m<g*,p>[(g*-m)g*-m/g*g* +c (h*+g*-m)h*+g*-m/(h+g*)h+g]mm, and one of the following conditions is fulfilled: 1) h* >g*, p+q> c*(h*-g*)h*-g*mm/g*g*.2)g>c* (h*+g)h*+gmm/(h*+g+m)h*+g+m, then this equation is oscillatory.